In mechanism design with symmetrical or asymmetrical motions, obtaining high precision of the input path given by working requirements of mechanisms can be a challenge for dimensional optimization. This study proposed a novel hybrid-combined differential evolution (DE) and Jaya algorithm for the dimensional synthesis of four-bar mechanisms with symmetrical motions, called HCDJ. The suggested algorithm uses modified initialization, a hybrid-combined mutation between the classical DE and Jaya algorithm, and the elitist selection. The modified initialization allows generating initial individuals, which are satisfied with Grashof’s condition and consequential constraints. In the hybrid-combined mutation, three differential groups of mutations are combined. DE/best/1 and DE/best/2, DE/current to best/1 and Jaya operator, and DE/rand/1, and DE/rand/2 belong to the first, second, and third groups, respectively. In the second group, DE/current to best/1 is hybrid with the Jaya operator. Additionally, the elitist selection is also applied in HCDJ to find the best solutions for the next generation. To validate the feasibility of HCDJ, the numerical examples of the symmetrical motion of four-bar mechanisms are investigated. From the results, the proposed algorithm can provide accurate optimal solutions that are better than the original DE and Jaya methods, and its solutions are even better than those of many other algorithms that are available in the literature.

This paper presents a general framework to design a cam profile using the finite element method from given displacements of the follower. The arbitrarily complex cam profile is described by Lagrangian finite elements, which are formed by the connectivity of nodes. In order to obtain the desired profile, a penalty-type functional that enforces the prescribed displacement of the follower is proposed. Additionally, in order to ensure convexity of the functional, a numerical stabilization scheme is used. The nodal positions are then obtained by solving a nonlinear system of equations resulting from minimizing the total functional. The geometrical accuracy of the cam profile can be controlled by the number of finite elements. A case study is considered to illustrate the flexibility, accuracy, and robustness of the proposed approach.